Speed & Motion

Who is faster, a cheetah or a high-speed train? Depends what you compare. Off the mark, a cheetah hits 60 km/h within two or three seconds; over the long haul, a cheetah needs a long rest after half a minute of sprinting, while the train cruises at 300 km/h all day. To compare speed fairly, we need one common ruler.

Speed = distance ÷ time

Speed = distance ÷ time — how far you travel in each unit of time.

Two unit systems are common: car dials read in kilometres per hour (km/h), physics labs prefer metres per second (m/s). The key to converting is that 1 hour = 3600 s and 1 km = 1000 m; bundle them together and you get:

$72 \div 3.6 = 20$

so 72 km/h = 20 m/s. Rule of thumb: from km/h to m/s, divide by 3.6; the other way, multiply by 3.6.

Align the units first

Metres with seconds give m/s. Confirm the units agree before you divide — most speed mistakes are really unit mistakes.

Distance-time graphs: read speed at a glance

Time runs along the bottom, distance up the side, and motion becomes a line:

the steeper the line, the faster the motion;
a flat stretch: time passes, distance doesn't — stopped;
a line heading down: travelling back.

Steep and gentle are just slope — you already met it in Equation of a Straight Line.

InteractiveRace Simulator

🏃 Runner A speed6🐢 Runner B speed4

s = v·t → A: 6×0.0 = 0.0 m · B: 4×0.0 = 0.0 m

Send two runners onto the track and tune their speeds to watch the lines turn steep or gentle. Who crosses the finish first is plain from the graph.

Average vs instantaneous speed

A trip hides two kinds of speed inside it. Cover 120 km in 3 hours and your average speed is $120 \div 3 = 40$ km/h — yet along the way you crawled at 0 in jams and touched 100 on open road. The number bouncing on the speedometer is instantaneous speed.

Average speed is not the average of speeds

Average speed = total distance ÷ total time, not the mean of several speeds. Drive 60 km in 1 hour (60 km/h), then 60 km in 2 more hours (30 km/h): the average is $\dfrac{120}{3} = 40$ km/h, not $\dfrac{60+30}{2} = 45$ .

Worked example: the 100-metre dash

A student finishes 100 m in 12.5 s. What is the average speed?

Compute the speed: $100 \div 12.5 = 8$ , that is 8 m/s;
Convert the units: $8 \times 3.6 = 28.8$ , that is 28.8 km/h.

Elite male sprinters average more than 10 m/s over 100 m; for a student, 8 m/s is already outstanding.

Check yourself

Quick quiz

1. 36 km/h is how many m/s?
2. A flat stretch appears on a distance-time graph. The runner is…
3. Runner A does 100 m in 12.5 s; runner B does 400 m in 50 s. Who is faster?